THE COUNTERPART OF A RESULT OF WEBB FOR THE BOUNDED DUAL Eb

Denote by E, E+ andEb the continuous dual, the sequential dual and the bounded dual, respectively, of the lcs(E,τ). Well-known is that, [1, 22.2, p.87][2. Proposition 2.5.7, p.107], f ∈ E ⇐⇒ kerf is closed. John Webb added that, [5, Proposition 1.9., p.345], f ∈ E+ ⇐⇒ kerf is sequentially closed. I, hereby, add that f ∈ Eb ⇐⇒ kerf is locally closed. The result substantially improves             [4, Proposition 6.2.15, p.177] A sequentially closed              hyperplane of a bornological space is closed.to a locally closed hyperplane of a semibornological space is closed.